Aiming to find magnetic states in the $M_{n+1}A{X}_n$ phases, we measured the magnetic susceptibility, the resistivity, and nuclear magnetic resonance of Cr${}_2$Ga$X$ ($X=\text{N}$ and C). Zero-field and longitudinal-field muon spin relaxation experiments were also applied to Cr${}_2$GaN. A magnetic phase transition, most probably to the spin-density-wave (SDW) state, has been found in Cr${}_2$GaN at $T_{\mathrm{N}}=170$ K in contrast to the Pauli paramagnetism in the carbide counterpart Cr${}_2$GaC. The origin of the SDW transition is interpreted in terms of possible Fermi-surface nesting in the two-dimensional-like electronic structure.

We have investigated the low-temperature physical properties of ${\mathrm{BaTi}}_2{\mathrm{Sb}}_2\mathrm{O}$ and ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Ti}}_2{\mathrm{Sb}}_2\mathrm{O}$ ($x=0.05$, 0.1, 0.15, 0.2, 0.25, 0.3) by means of muon spin rotation ($\mu$SR) and SQUID magnetometry. Our measurements reveal the absence of magnetic ordering below $T_{\mathrm{DW}}=58$ K in the parent compound. Therefore the phase transition at this temperature observed by magnetometry is most likely due to the formation of a charge-denisty wave (CDW). Upon substitution of barium by sodium in ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Ti}}_2{\mathrm{Sb}}_2\mathrm{O}$ we find for $x=0.25$ superconductivity with a maximum $T_c=5.1$ K in the magnetization and a bulk $T_{c,\mathrm{bulk}}=4.5$ K in the $\mu$SR measurements. The temperature dependency of the London penetration depth ${\lambda }^{-2}\left(T\right)$ of the optimally doped compound can be well explained within a conventional weak-coupling scenario in the clean limit.

X-ray coherent diffraction imaging including ptychography provides the nanoscale resolved three-dimensional description of matter. The combination of these approaches to the Bragg geometry case arouses a strong interest for its capability to provide information about strain state in crystals. Among the existing approaches, ptychography is particularly appealing because it allows the investigation of extended or weakly scattering samples. Coherent diffraction imaging approaches, based on redundancy in the collected diffraction intensity data set, are highly time consuming and rely on state-of-the-art mechanical setups, both being strong limitations for a general application. We show here that these can be overcome by regularization-based inversion algorithms introducing a priori structural knowledge. This method, which can be generalized to other wavelengths or beam sources, opens new possibilities for the imaging of radiation-sensitive specimens or very large samples.

The temperature-dependent effective potential (TDEP) method is generalized beyond pair interactions. The second- and third-order force constants are determined consistently from ab initio molecular dynamics simulations at finite temperature. The reliability of the approach is demonstrated by calculations of the mode Grüneisen parameters for Si. We show that the extension of TDEP to a higher order allows for an efficient calculation of the phonon life time, in Si as well as in $\epsilon$-FeSi; a system that exhibits anomalous softening with temperature.

The midinfrared anomalous Hall effect (AHE) can provide critical new information for resolving the controversial origins of the dc AHE in Ca${}_x$Sr${}_{1-x}$RuO${}_3$. The complex Faraday and Kerr angles, as well as the complex Hall conductivity ${\sigma }_{xy}$, are measured in Ca${}_x$Sr${}_{1-x}$RuO${}_3$ films as a function of mid- and near-infrared energy $E$ from 0.1 eV to 1.4 eV, magnetic field $H$, temperature $T$, and Ca concentration $x$. For the ferromagnetic state from $x=0$ to 0.4, the $(d_{xz},d_{yz})$-orbital tight-binding model is employed to investigate the quasiparticle role in the low energy response of the AHE ${\sigma }_{xy}\left(E\right)$ since the Berry curvature term becomes weak at low energies. The infrared Hall sign reversals with $T$ are observed only at $x=0$ and 0.13, which is narrower than the Ca concentration range in which the dc Hall sign reversal appears. The similarity of the infrared Hall angles between paramagnetic and ferromagnetic Ca${}_x$Sr${}_{1-x}$RuO${}_3$ compounds demonstrates the symmetric nature of the Hall response around the quantum phase transition at $x=0.7$.

Electronic structures, minimum energy configurations, and band topology of strained Bi(111) single bilayers placed on a variety of semiconducting and insulating substrates are investigated using first-principles calculations. A topological phase diagram of a free-standing Bi bilayer is presented to help guide the selection of suitable substrates. The insulating hexagonal-BN is identified as the best candidate substrate material for supporting nontrivial topological insulating phase of Bi bilayer thin films. A planar hexagonal Bi layer is predicted under tensile strain, which we show could be realized on a SiC substrate. The Bi bilayer becomes metallic under the compressive strain induced by Si and Ge substrates.

We investigate the electronic and thermodynamic properties of Zr and its oxides from first principles to elucidate phase stability in the Zr-O system. Hexagonally close-packed Zr is unusual in its ability to dissolve very high concentrations of oxygen over its interstitial octahedral sites, forming a variety of ordered suboxides that undergo both first-order and second-order phase transitions upon heating. We perform a first-principles, statistical-mechanical analysis of finite temperature phase stability of ZrO${}_x$ using a cluster expansion Hamiltonian and Monte Carlo calculations. This analysis predicts the existence of 0-K ground-state oxygen orderings at composition ZrO${}_{1/6}$, ZrO${}_{2/9}$, ZrO${}_{1/3}$, ZrO${}_{4/9}$, and ZrO${}_{1/2}$ along with evidence of an infinite sequence of ground-state suboxide orderings at intermediate oxygen concentrations consisting of different stackings of empty, $\frac{1}{3}$-filled and $\frac{2}{3}$-filled two-dimensional oxygen layers. We also predict the stability of a previously uncharacterized Zr-monoxide phase, which we label ${\delta }^{\prime }$-ZrO due to its crystallographic relation to $\delta$-TiO. The ${\delta }^{\prime }$-ZrO structure is equivalent to the high-pressure $\omega$-Zr phase but has interstitial oxygen ordering. Finally, as part of the technical implementation of our statistical mechanical study, we introduce a new algorithm to parametrize the coefficients of a cluster expansion Hamiltonian and apply a $k$-space analysis to rigorously track order-disorder phenomena at finite temperature.

We carry out a numerical study of the bipartite entanglement entropy in the gapped regime of two paradigmatic quantum spin chain models: the Ising chain in an external magnetic field and the antiferromagnetic XXZ model. The universal scaling limit of these models is described by the massive Ising field theory and the $SU\left(2\right)$-Thirring (sine-Gordon) model, respectively. We may therefore exploit quantum field theoretical results to predict the behavior of the entropy. We numerically confirm that in the scaling limit, corrections to the saturation of the entropy at large region size are proportional to a modified Bessel function of the first kind, $K_0\left(2mr\right)$, where $m$ is a mass scale (the inverse correlation length) and $r$ the length of the region under consideration. The proportionality constant is simply related to the number of particle types in the universal spectrum. This was originally predicted by J. L. Cardy, O. A. Castro-Alvaredo, and B. Doyon [J. Stat. Phys. 130, 129 (2008)] and B. Doyon [Phys. Rev. Lett. 102, 031602 (2009)] for two-dimensional quantum field theories. Away from the universal region our numerics suggest an entropic behavior following quite closely the quantum field theory prediction, except for extra dependencies on the correlation length.

Magnetic and magnetocaloric properties of high-purity, giant magnetocaloric polycrystalline and single-crystalline Fe${}_2$P are investigated. Fe${}_2$P displays a moderate magnetic entropy change, which spans over 70 K and the presence of strong magnetization anisotropy proves this system is not fully itinerant but displays a mix of itinerant and localized magnetism. The properties of pure Fe${}_2$P are compared to those of giant magnetocaloric (Fe,Mn)${}_2$(P,$A$) (where $A=\text{As}$, Ge, Si) compounds helping understand the exceptional characteristics shown by the latter, which are so promising for heat pump and energy conversion applications.

We studied magnetism of Sr${}_2$ScO${}_3$CoAs, a member of the group of layered compound with CoAs conducting layers, by using successfully synthesized polycrystalline sample. As a result of magnetic and electric resistivity measurements, Sr${}_2$ScO${}_3$CoAs was revealed to be an itinerant electronic ferromagnet with the Curie temperature $T_{\mathrm{C}}$ $=$ 48 K. We discussed the magnetism of this compound within the spin fluctuation theory for three-dimensional itinerant electronic ferromagnets in the ordered state and also pointed out possible quasi-two-dimensional behavior observed in magnetism.

We show that the newly discovered ${\mathrm{BiS}}_2$-based superconductors may have a dominant triplet pairing component in addition to a subdominant singlet component arising from the spin-orbital coupling. The pairing respects time-reversal symmetry. The dominant triplet gap causes gap sign changes between the spin-split Fermi pockets. Within a pocket, the gap function respects $d_{x^2-y^2}^{*}$-wave symmetry where the asterisk indicates joint spin-lattice rotations. Below the Lifshitz filling level, the gap is nodeless, and the superconducting state is weak topological. Above the Lifshitz points, the gap becomes nodal. The superconducting pairing and the time-reversal symmetry result from the strong spin-orbital coupling and the ferromagneticlike spin fluctuations. The $d_{x^2-y^2}^{*}$-wave gap structure follows from the coexisting antiferromagnetic spin fluctuations. The relevance to experiments is discussed.

We consider the problem of the orbital upper critical magnetic field, parallel to the most conducting axis of a quasi-one-dimensional layered superconductor. It is shown that superconductivity can be destroyed through orbital effects at fields much higher than the so-called Clogston-Chandrasekhar paramagnetic limiting field $H_p$, provided that superconducting pairing of electrons are of a triplet nature. We demonstrate that the superconducting state of the quasi-one-dimensional layered conductor ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$ is well described by the suggested theory. To this end, we consider two competing scenarios: (1) a superconducting order parameter without zeros on the Fermi surface, and (2) one with zeros on the Fermi surface—both are shown to lead to destruction of superconductivity at a magnetic field $H_{c_2}^x$, five times higher than $H_p$. With recent experimental measurements on the ${\mathrm{Li}}_{0.9}{\mathrm{Mo}}_6{\mathrm{O}}_{17}$ favoring the nodeless order parameter, we present a strong argument supporting triplet pairing in this compound.

Alkali-metal-intercalated FeSe materials, (NH${}_3$)${}_{\mathrm{y}}$$M_{0.4}$FeSe ($M$: K, Rb, and Cs), have been synthesized using the liquid NH${}_3$ technique. (NH${}_3$)${}_{\mathrm{y}}$Cs${}_{0.4}$FeSe shows a superconducting transition temperature ($T_{\mathrm{c}}$) as high as 31.2 K, which is higher by 3.8 K than the $T_{\mathrm{c}}$ of nonammoniated Cs${}_{0.4}$FeSe. The $T_{\mathrm{c}}$s of (NH${}_3$)${}_{\mathrm{y}}$K${}_{0.4}$FeSe and (NH${}_3$)${}_{\mathrm{y}}$Rb${}_{0.4}$FeSe are almost the same as those of nonammoniated K${}_{0.4}$FeSe and Rb${}_{0.4}$FeSe. The $T_{\mathrm{c}}$ of (NH${}_3$)${}_{\mathrm{y}}$Cs${}_{0.4}$FeSe shows a negative pressure dependence. A clear correlation between $T_{\mathrm{c}}$ and lattice constant $c$ is found for ammoniated metal-intercalated FeSe materials, suggesting a correlation between Fermi-surface nesting and superconductivity.

Superconductivity in alkali-intercalated iron selenide, with $T_c$'s of $30\mathrm{K}$ and above, may have a different origin than that of the other Fe-based superconductors, since it appears that the Fermi surface does not have any holelike sheets centered around the $\Gamma$ point. Here we investigate the symmetry of the superconducting gap in the framework of spin-fluctuation pairing calculations using density functional theory bands downfolded onto a three-dimensional (3D), ten-orbital tight-binding model, treating the interactions in the random-phase approximation (RPA). We find a leading instability towards a state with $d$-wave symmetry, but show that the details of the gap function depend sensitively on electronic structure. As required by crystal symmetry, quasinodes on electron pockets always occur, but are shown to be either horizontal, looplike, or vertical depending on details. A variety of other 3D gap structures, including bonding-antibonding $s$-symmetry states which change sign between inner and outer electron pockets, are found to be subdominant. We then investigate the possibility that spin-orbit coupling effects on the one-electron band structure, which lead to enhanced splitting of the two $M$-centered electron pockets in the 2-Fe zone, may stabilize the bonding-antibonding $s_{\pm }$-wave states. Finally, we discuss our results in the context of current phenomenological theories and experiments.

We show by first-principles calculations that high-pressure confinement suppresses the usual ambient or low-pressure deformation modes for compressed graphite toward low-density phases under large shear deformation and promotes alternative structural evolution to high-density phases that possess enhanced shear strength surpassing that of diamond. This finding explains the puzzling experimental observation of compressed graphite cracking diamond anvil [W. L. Mao et al., Science 302, 425 (2003)] and suggests different principles for determining material strength at high pressure. It also underscores the need to go beyond empirical hardness formulas that are unable to account for changes in pressure-constrained structural evolution and their influence on strength.

A general fluctuation-electrodynamic theory is developed to investigate radiative heat exchanges between objects that are assumed to be small compared with their thermal wavelength (dipolar approximation) in $N$-body systems immersed in a thermal bath. This theoretical framework is applied to study the dynamic of heating or cooling of three-body systems. We show that many-body interactions allow us to tailor the temperature field distribution and to drastically change the time scale of thermal relaxation processes.

We have investigated optical conductivity spectra of $n$- and $p$-type Ba${}_8$Ga${}_{16}$Sn${}_{30}$ ($\alpha$-BGS) with type-VIII clathrate structure, at temperatures from 296 K down to 6 K with a terahertz time-domain spectrometer (0.2–2.5 THz). The continuous spectra contributed from charge carriers are dispersive in this frequency range and also temperature and carrier-type dependent. The Drude-Smith model taking multiple scatterings of charge carriers into account well reproduces those data. The relaxation rate of the $n$-type carriers decreases more sharply than that in the $p$-type material, suggesting a stronger electron-phonon interaction in the $n$-type material than in the $p$-type. On the other hand, the localized infrared-active modes observed at 1.3 and 1.7 THz, identified as the rattling phonons of the Ba${}^{2+}$ ion quasi-on-center vibrations become soft and broad significantly with decreasing temperature as well as observed in type-I BGS and BGG (Ba${}_8$Ga${}_{16}$Ge${}_{30}$) clathrates. The softening in the $n$-type material is smaller by about 30% than in the $p$-type one, whereas the linewidth broadening is almost independent of the carrier type. The difference in the softening is discussed with a scenario where the interaction of rattling phonons with carriers can modify the anharmonic potential of the guest ions. The anomalous broadening at low temperatures is also discussed with the use of the impurity-scattering model presented for a rattling-phonon system strongly hybridized with acoustic cage phonons.

We study response to a twist in the two-dimensional $p$-state clock model, which has the discrete $Z_p$ symmetry. The response is measured in terms of helicity modulus, which is usually defined with respect to an infinitesimal twist. However, we demonstrate that such a definition is inappropriate for the clock model. The helicity modulus must be defined with respect to a finite, quantized twist which matches the discrete $Z_p$ symmetry of the model. Numerical study of the appropriately defined helicity modulus resolves controversy over the clock model, showing the existence of two Berezinskii-Kosterlitz-Thouless transitions for $p>4$.

The ferromagnetic phase of Ca${}_2$RuO${}_4$ has been puzzling because the observed magnetic moment $m$ $\approx$ 0.4${\mu }_B$/Ru is surprisingly small, compared with the predicted 2${\mu }_B$/Ru. This discrepancy is resolved by considering the interplay of the spin-orbit coupling and Coulomb repulsion, which results in a large enhancement of the spin-orbit splitting. A simple tight-binding formula shows that the moment reduction originates in the competition between the spin-orbit coupling and magnetic exchange splitting. This competitive picture provides a unified explanation for the complicated phase diagram of Ca${}_2$RuO${}_4$, including the antiferromagnetic insulating, paramagnetic insulating, and ferromagnetic metallic phase.